{
  "abstract": "We characterize boundedness of the Bergman projection on operator-weighted $L^p$ spaces over a separable Hilbert space, for $1<p<\\infty$. Under the directional integrability conditions, the criterion is uniform boundedness of averages over Carleson squares in the unit disc. We obtain norm estimates independent of dimension. The proof uses a separated kernel expansion and a layer decomposition of the tent tree. No reverse Hölder assumption is needed. We also give a finer matrix estimate with a dimension-dependent constant. Boundedness is unchanged by compactly supported changes of the weight that preserve the integrability conditions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28521",
  "author_total": 2,
  "authors": [
    {
      "name": "Xu Chunxu"
    },
    {
      "name": "Dong Jianxiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ayjtbz03sb8eb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28521",
  "fulltext_url": null,
  "id": "ayjtbz03sb8eb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28521",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7214294371",
  "pdf_url": "https://arxiv.org/pdf/2609.28521",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ayjtbz03sb8eb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.28521",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28521"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Bergman projection with operator weights",
  "title_text": "The Bergman projection with operator weights",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/ayjtbz03sb8eb",
  "venue": "arXiv",
  "versions": []
}